The health minister, Peter Dutton, has expressed confidence in his ability to reach a deal with doctors and crossbench senators over his Medicare co-payment plans, but there are no clear signs of a breakthrough in the budget stalemate.

Dutton emerged from talks with the Australian Medical Association (AMA) saying he was willing to compromise if amendments improved the government’s proposal, yet he reaffirmed his belief that $7 was “a reasonable price for people to pay when they go to see a doctor”.

The Palmer United party (PUP) leader, Clive Palmer, poured cold water on the prospect of a deal. He told Guardian Australia on Friday his senators were firmly against any Medicare co-payment, ruled out agreement on any possible changes, and said the government was engaged in “wishful thinking” for believing the measure would pass the Senate.

Labor and the Greens reaffirmed their opposition to the proposal as a matter of principle, indicating that tweaking would fail to secure adequate upper house support.

The co-payment is one of numerous contentious budget measures that face defeat after the opposition and other parties vowed to oppose the “unfair” proposals. On Friday the treasurer, Joe Hockey, suggested budget critics should take a “chill pill” as he continued a new round of talks with crossbench senators to chart a way forward.

Hockey met with the Tasmanian PUP senator Jacqui Lambie, who told him the party would “hold firm” against budget savings that would hurt average Australian households. But Lambie said she had suggested during the 2.5 hour meeting that the government make even greater cuts to foreign aid. The Coalition has already budgeted foreign aid savings of $7.6bn over five years – a measure that does not require legislation.

In an interview, Hockey said many commentators and critics were “impatient” when it came to dealing with issues before the parliament, but the government would work in a methodical way because it was “a marathon not a sprint”.

He said the biggest savings in the budget had come from reduced appropriations in areas that did not require additional specific legislation.

“So it’s important that everyone has a bit of a chill pill here and understands that the budget is a long-term structural plan to address Labor’s deficit and debt and importantly to build the infrastructure necessary to build a stronger and more productive economy with more jobs,” Hockey told Sky News.

The opposition leader, Bill Shorten, said: “Treasurer, if you are a pensioner worried about having your pension cut, if you are a mum worrying about how you’ll be able to afford to take your kids to the doctor and pay the GP tax, if you’re working-class parents – perhaps you work at Alcoa and you’ve just lost your job and you’re worrying about how on earth you’re going to pay for your kids to go to university – the one thing you don’t need is an arrogant, out-of-touch treasurer telling people just to take a chill pill.”

Both Dutton and Owler described the meeting as productive, although more talks were needed.

The AMA wants substantial changes, including no reduction in Medicare benefits schedule rebates, and has argued against linking the proceeds to the government’s new medical research future fund. It wants amendments to protect the elderly, the chronically ill, the poor, and Indigenous Australians from the “harmful impact”.

The government had already indicated that patients with concession cards and children under 16 would attract the co-payment for only the first 10 services each year.

Owler said the AMA’s “fairer and more equitable” plan would not deliver the $3.5bn over five years that the government had sought because it was “a health policy, not an economic policy”.

“The minister has agreed to have his office and his department examine our alternative proposals,” Owler said.

Dutton said the government was “dead keen on making sure that Medicare is sustainable” and would continue discussions with the AMA, senators and other stakeholders aimed at “seeing the safe passage of the $7 co-payment through the Senate”.

“It will be some time I think before we can arrive at a deal but I think a deal can be done and I think that is because people want to see Medicare strengthened,” Dutton said. “I honestly believe this is in the best interests of our health system.”

Labor seized on Dutton’s comment that he had held discussions with the AMA before the election about “the government’s interest in a co-payment” – but the minister’s office said he had meant to say “before the budget”.

An AMA source confirmed the minister had held pre-budget talks about the consultant Terry Barnes’ co-payment proposal, aired in a submission to the commission of audit, but said discussions about the government’s intended model did not occur until after the budget.

Palmer said Australia’s health system was much more efficient than the one in the US, and the PUP senators were united in their opposition to any Medicare co-payment on the basis it “crosses the Rubicon” on access to free healthcare. “No, we don’t want any co-payment at all: zero dollars,” he said.

Asked to rule out a compromise deal, Palmer said: “Yes, absolutely. It’s not a question of how many people die, how many senior citizens do you put in anguish to make Tony Abbott and Peter Dutton happy; I didn’t get elected to parliament to do that. Jacqui Lambie, Dio Wang, Glenn Lazarus, Ricky Muir – they’re all of the same view.”

Earlier, Dutton gave an insight into the government’s thinking on the principle of bulk billing, saying it should “be about helping those that can’t afford the $7, not a business tool for some doctors – for argument’s sake – to try and take market share from the doctor down the road”.

“I want it to be used as a safety net for people, not as a level of expectation that’s built up over a period of time,” Dutton told the Brisbane radio station 4BC.

The Greens senator Richard Di Natale said universality regardless of wealth was a crucial principle of Medicare, ensuring people could seek care without barriers at the point of access.

“At least he [Dutton] is being honest and saying he doesn’t support universality when it comes to Medicare,” Di Natale said.